[Alta-Logic] Peripatetic Seminar Invited Lecture Series

[Jonathan Gallagher]

We are pleased to announce that the next
speaker in the Peripatetic Seminar Invited Lecture Series
is Geoff Cruttwell, speaking tomorrow at 5pm in
ICT 616.  Details below.


*Speaker*: Geoff Cruttwell
*Title*: Affine spaces in a tangent category
*Location*: ICT 616, November 6 at 5 pm.
*Abstract*:

Affine manifolds are smooth manifolds with a particular choice of charts
such that each transition function is affine.  In addition to being
interesting in their own right, recent work of Jubin showed that the
category of affine manifolds has a wide variety of monads and comonads on
it, with many distributive laws relating these monads and comonads.

In this talk, we shall see how to work with affine manifolds in a tangent
category.    A key result of Auslander and Markus shows that an affine
structure on a smooth manifold M is equivalent to giving a flat,
torsion-free connection on the tangent bundle of M; this we take as the
definition of an affine object in a tangent category.  We give several
alternate characterizations of such connections (some of which appear to be
new in differential geometry), show how to extend Jubin's results on the
existence of monads and comonads to this setting, and find additional
distributive laws between these monads and comonads that Jubin did not
discover.

This is joint work Rick Blute and Rory Lucyshyn-Wright.

See also http://peripatetic-seminar.cpsc.ucalgary.ca/wp/
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